Question

find sin (45 + theta) - Cos (45 - theta)

Answer 1

we know that

$\sin( \alpha + \beta ) = \sin( \alpha ) \cos( \beta ) + \cos( \alpha ) \sin( \beta ) \\ and \\ \cos( \alpha - \beta ) = \cos( \alpha ) \cos( \beta ) + \sin( \alpha ) \sin( \beta )$

using it, we get

$\sin(45 + \theta) - \cos(45 - \theta) \\ = \sin(45) \cos( \theta) + \cos(45) \sin( \theta) \\ \: \: \: - \cos(45) \cos( \theta) - \sin(45) \sin( \theta ) \\ = 0$